Calculator Skills (Papers 2 & 3)

Papers 2 and 3 both allow calculator use, but having a calculator does not mean every question is straightforward. You need to use your calculator efficiently and know its functions well. This lesson covers essential calculator techniques for the Edexcel GCSE.

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Know Your Calculator

You should be using a scientific calculator — not a basic one. Popular models include the Casio fx-83GT CW, Casio fx-85GT CW, or equivalent.

Key Buttons You Must Know

Button/Function	What it does	When to use it
a b/c or fraction key	Enters proper and improper fractions	Fraction questions
$x^{2}$x2 and $x^{3}$x3	Squares and cubes a number	Powers, Pythagoras
$x^{n}$xn or ^	Raises to any power	Indices, compound interest
$\sqrt{\phantom{x}}$x​ and $\sqrt[3]{\phantom{x}}$3x​	Square root and cube root	Surds, Pythagoras
( )	Brackets	Controlling order of operations
sin / cos / tan	Trigonometric functions	Trigonometry questions
$\sin^{-1} / \cos^{-1} / \tan^{-1}$sin−1/cos−1/tan−1 (SHIFT + sin/cos/tan)	Inverse trig functions	Finding angles
$\pi$π	The value of pi	Circle calculations
ANS	Last answer	Chaining calculations
STO / RCL or M+ / M−	Memory storage and recall	Storing intermediate values
S⟺D	Switches between surd/fraction and decimal	Giving exact or decimal answers
$\times10^{x}$×10x or EXP	Standard form entry	Standard form calculations
(−) or neg	Negative numbers	Substitution with negatives

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Using Brackets Correctly

The most common calculator error is failing to use brackets where needed. Your calculator follows the order of operations (BIDMAS/BODMAS), so you must force the correct grouping.

Worked Example 1 — Division by a Sum

Calculate $(5 + 7) \div (3 + 1)$(5+7)÷(3+1).

Wrong entry: $5 + 7 \div 3 + 1 = 5 + 2.333$5+7÷3+1=5+2.333... + 1 = 8.333... (WRONG) Correct entry: $(5 + 7) \div (3 + 1) = 12 \div 4 =$(5+7)÷(3+1)=12÷4= 3

Worked Example 2 — Negative Numbers in Substitution

Find the value of $3x^{2} - 2x + 1$3x2−2x+1 when x = −4.

Correct entry: $3 \times (-4)^{2} - 2 \times (-4) + 1 = 3 \times 16 + 8 + 1 =$3×(−4)2−2×(−4)+1=3×16+8+1= 57

Common mistake: Entering $3 \times -4^{2}$3×−42 gives $3 \times (-16) = -48 ($3×(−16)=−48(the calculator squares before applying the negative).

Worked Example 3 — The Quadratic Formula

Solve $2x^{2} - 7x + 3 = 0$2x2−7x+3=0 using the quadratic formula.

$x = (7 \pm \sqrt{49 - 24}) / 4 = (7 \pm \sqrt{25}) / 4 = (7 \pm 5) / 4$x=(7±49−24​)/4=(7±25​)/4=(7±5)/4

Calculator entry for the first root: $(7 + \sqrt{49 - 24}) \div 4$(7+49−24​)÷4 Make sure the entire numerator is in brackets: $(7 + \sqrt{49 - 24}) \div 4 = 3$(7+49−24​)÷4=3

Calculator entry for the second root: $(7 - \sqrt{49 - 24}) \div 4 =$(7−49−24​)÷4= 0.5

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Storing Values in Memory

When a calculation produces an intermediate result you need later, store it rather than rounding and re-entering.

Worked Example 4

A circle has circumference 47.3 cm. Find its area.

Step 1: Find the radius. $C = 2\pi r \to r = 47.3 \div (2\pi)$C=2πr→r=47.3÷(2π) Calculator: $47.3 \div (2 \times \pi) = 7.52817$47.3÷(2×π)=7.52817... Store this: Press STO then A (or M+)

Step 2: Find the area. $A = \pi r^{2} = \pi \times (7.52817...)^{2}$A=πr2=π×(7.52817...)2 Calculator: $\pi \times$π× RCL $A^{2} ($A2(or $\pi \times$π× ANS$^{2})$2) = $178.1 cm^{2}$178.1cm2 (to 1 d.p.)

If you had rounded r to 7.53 and used that: $\pi \times 7.53^{2} = 178.16$π×7.532=178.16... — a slight difference that could cost you an accuracy mark.

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Standard Form on Your Calculator

Entering Standard Form

To enter $3.2 \times 10^{5}$3.2×105:

• Press 3.2 then the $\times10^{x}$×10x button then 5.
• Do NOT press $3.2 \times 10 ^ 5 ($3.2×105(this can give the wrong result on some calculators).

Reading Standard Form from the Display

Your calculator may display $3.2_{5}$3.25​ or 3.2 E 05 or $3.2 \times 10^{5}$3.2×105 depending on the model. Know what your calculator's notation means.

Worked Example 5

$(4.8 \times 10^{7}) \div (1.6 \times 10^{3})$(4.8×107)÷(1.6×103)

Enter: $4.8 \times10^{x} 7 \div 1.6 \times10^{x} 3 =$4.8×10x7÷1.6×10x3= $3 \times 10^{4}$3×104 (or 30000)

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Trigonometry on the Calculator

Ensure Correct Mode

Always check your calculator is in DEGREE mode (not radians or gradians) for GCSE. Look for a small "D" or "DEG" on the display.

Finding a Side

Worked Example 6

In a right-angled triangle, the hypotenuse is 12 cm and one angle is $35°$35°. Find the opposite side.

$\sin 35° =$sin35°= opposite / 12 opposite $= 12 \times \sin 35°$=12×sin35° Calculator: $12 \times \sin(35) =$12×sin(35)= 6.88 cm (to 3 s.f.)

Finding an Angle

Worked Example 7

In a right-angled triangle, the opposite side is 5 cm and the adjacent side is 8 cm. Find the angle.

$\tan \theta = 5/8$tanθ=5/8 $\theta = \tan^{-1}(5/8)$θ=tan−1(5/8) Calculator: SHIFT $\tan (5 \div 8) =$tan(5÷8)= $32.0°$32.0° (to 1 d.p.)

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Checking Reasonableness

Always ask: "Does my calculator answer make sense?"

Quick Checks

• Percentages should be between 0 and 100 in most contexts.
• Angles in a triangle must add up to $180°$180°.
• Lengths and areas must be positive.
• An area should be larger than the square of the smallest dimension but not absurdly large.
• If you calculated compound interest, the final amount should be more than the original (for growth) or less (for depreciation).

Example

You calculate that a 20% discount on £85 gives £17. Check: 10% of £85 = £8.50, so 20% = £17. Correct.

You calculate the area of a circle with radius 5 cm as $78.5 cm^{2}$78.5cm2. Check: $\pi \times 25 \approx 3.14 \times 25 \approx 78.5$π×25≈3.14×25≈78.5. Correct.

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The S⟺D Button

This button switches between exact forms (fractions, surds, multiples of $\pi)$π) and decimal approximations.

Example: Calculate $1 \div 7$1÷7. Display shows: 1/7 (exact) Press S⟺D: shows 0.142857...

When to use exact form: When the question says "give your answer as a fraction" or "in terms of $\pi$π." When to use decimal: When the question says "give your answer to 2 decimal places" or "3 significant figures."

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Practice Problems